Well logging provides various parameters that may be used to determine the "quality" of a formation from a given borehole. These parameters include such factors as: resistivity, porosity, permeability and bound fluid volume (BFV). The parameters may be used to determine the amount of hydrocarbons present within the formation, as well as provide an indication as to the difficulty in extracting those hydrocarbons from the formation. BFV, in general, represents the volume of fluid that normally cannot be extracted from the formation (versus free fluid volume--the volume of fluid that will flow through the pores of the formation and thus, may be extracted). BFV is therefore, an important factor in determining whether a specific well site is commercially viable.
There are various known techniques for determining BFV. For example, it is known to apply nuclear magnetic resonance (NMR) techniques to measure BFV. NMR measurements, in general, are accomplished by causing the magnetic moments of nuclei in a formation to precess about an axis. The axis about which the nuclei precess may be established by applying a strong, polarizing, static magnetic field (B.sub.0) to the formation, such as through the use of permanent magnets. This field causes the proton spins to align in a direction parallel to the applied field (this step, which is sometimes referred to as the creation of longitudinal magnetization, results in the nuclei being "polarized"). Polarization does not occur immediately, but instead grows in accordance with a time constant T.sub.1, as described more fully below, and may take as long as several seconds to occur (even up to about eight seconds). After sufficient time, a thermal equilibrium polarization (M.sub..infin.) parallel to B.sub.0 has been established (i.e., M.sub..infin. is proportional to B.sub.0)
Next, a series of radio frequency (RF) pulses are produced so that an oscillating magnetic field, B.sub.1, is applied. The first RF pulse (referred to as the 90.degree. pulse) must be strong enough to rotate the magnetization from B.sub.0 substantially into the transverse plane (i.e., transverse magnetization). The rotation angle is given by: EQU .alpha.=.gamma.B.sub.1 t.sub.p (1)
(where t.sub.p is the pulse length) and is adjusted to be 90.degree.. Additional RF pulses, preferably a .alpha.=180.degree. (referred to as 180.degree. pulses), are applied to create a series of spin echos. The frequency of the RF pulses is chosen to excite specific nuclear spins of a particular region of the sample that is being investigated. The rotation angles of the RF pulses are adjusted to be 90.degree. and 180.degree. in the center of this region.
Two time constants are associated with the relaxation processes of the longitudinal and transverse magnetization. These time constants characterize the rate of return to thermal equilibrium of the magnetization components following the application of each 90.degree. pulse. The spin-lattice relaxation time (T.sub.1) is the time constant for longitudinal magnetization to return to its thermal equilibrium value M.sub..infin. in the static magnetic field. The spin-spin relaxation time (T.sub.2) is the time constant for the transverse magnetization to return to its thermal equilibrium value which is zero. In addition, B.sub.0 is typically inhomogeneous and the transverse magnetization decays with the shorter time constant T.sub.2 *, where: ##EQU1##
but the part decaying with T, which is due to the inhomogeneous B.sub.0, can be recovered by refocusing pulses that produce the echos.
The most common method for determining BFV involves determining the entire fully polarized T.sub.2 distribution and then computing results based on T.sub.2 values less than a fixed cutoff value (e.g., 33 milliseconds for sandstone). The portion of protons with T.sub.2 's smaller than the fixed cutoff represents the BFV, while the portion of protons with T.sub.2 's larger than the fixed cutoff represents the amount of free fluid in the formation.
Another known method for calculating BFV determines the entire T.sub.2 distribution for a given sample, and then computes the amplitude of the signal components with T.sub.2 values less than the "free fluid" cutoff value (or relaxation cutoff time). Instead of the traditional fixed cutoff, a tapered cutoff is theoretically determined that accounts for bound fluid volume lining large pores that would otherwise be considered to be free or extractable (see, R. L. Kleinberg et al., "Tapered Cutoffs for Magnetic Resonance Bound Fluid Volume," Society of Petroleum Engineers, Doc. No. SPE 38737, 1997) (the "Kleinberg theoretical analysis"). For example, previous determinations of bound fluid assume that the bound fluid occupies small pores and free fluid occupies large pores. It was then assumed that the large pores would empty so that any fluid therein was free fluid, not bound fluid. The Kleinberg theoretical analysis, however, found that under certain circumstances, such as in clean well-sorted sands and carbonates where fixed cutoff computations provide low bound fluid results, the tapered cutoff provides a more accurate measure of BFV.
Another way to determine BFV using a tapered cutoff is based on empirically derived tapered cutoffs rather than the theoretically determine d tapered cutoff described above. The derived tapered cutoff relates each relaxation time to a specific fraction of capillary bound water, assuming that each pore size has an inherent irreducible water saturation (see, G. R. Coates et al., "A New Characterization of Bulk-Volume Irreducible Using Magnetic Resonance," SPWLA 38th Annual Logging Symposium, Jun. 15-18, 1997) (the "Coates empirical analysis"). The Coates empirical analysis utilized permeability models that do not rely on a specific model of pore geometry t o relate irreducible water saturation (S.sub.WIRR) to the T.sub.2 distribution as follows: ##EQU2##
(where m and b a re empirical factors used for calibration of empirical data sets) which was then applied to different values of m with b=1, and different values of b with m=0.0618. In both the Kleinberg theoretical analysis and the Coates empirical analysis, the entire T.sub.2 distribution is used (rather than the cutoff method) to determine BFV, which is a direct output of the inversion of the echo data.
Another known method for calculating BFV using NMR is the fixed cutoff method which is described in commonly-assigned, Sezginer et al. U.S. Pat. No. 5,389,877 (Sezginer). Sezginer describes using NMR techniques in which a short train of spin echos (i.e., j echoes) are used to obtain a sharp cutoff (i.e, the fixed cutoff relaxation time T.sub.C) that can be used to determine the producible volume in a borehole by measuring bound fluid and subtracting it from total porosity. These NMR techniques apply a weighted sum of the echos to determine BFV as follows: ##EQU3##
(where w.sub.j is a weighting factor chosen to weight different T.sub.2 components differently to sharpen (i.e., make steeper) the produced cutoff curve, and the overbar represents an estimate of BFV). The estimator of BFV is a linear function that acts on the relaxation-time distribution: ##EQU4##
where .function.(T.sub.1) is a weighting function as follows: ##EQU5##
(where T.sub.r is the recovery time before a CPMG sequence, and t.sub.cp is the Carr-Parcell spacing). .function.(T.sub.1) is approximately equal to 0 if T.sub.1 is greater than T.sub.C, and approximately equal to 1 if T.sub.1 is less than T.sub.C. Sezginer assumes that the T.sub.1 /T.sub.2 ratio is approximately constant, being about unity for bulk water samples and about 1.5 for water saturated sandstones. A potential problem with the sharp cutoff of Sezginer may occur if the echo decays faster than predicted, for example, if motion of the measuring probe occurs during measurements. Under these conditions, the resultant data may be degraded.
While Sezginer assumes that the T.sub.1 /T.sub.2 ratio is approximately constant, the T.sub.1 /T.sub.2 ratio must be considered when a shortened wait time between NMR experiments (e.g., as set forth in Sezginer) is used in determining BFV. For example, it is known that the NMR signal from a fluid is proportional to the hydrogen index (HI) and T.sub.1 Effect (TOE Factor) as described by Kleinberg & Vinegar in "NMR Properties for Reservoir Fluids," The Log Analyst, Nov.-Dec. 1996. Kleinberg and Vinegar provide that the TOE Factor is defined as: EQU TOE Factor=[1-exp(-t.sub.r /T.sub.1)] (7)
(where t.sub.r is the wait time between NMR measurements and T.sub.1 is the longitudinal relaxation time, as described above). Kleinberg and Vinegar also showed that the signal for a given T.sub.2 may be determined as: EQU S(T.sub.2)=V.sub.water (T.sub.2).times.HI.sub.water.times.[1-exp (-t.sub.r /T.sub.1water)] EQU +V.sub.oil (T.sub.2).times.HI.sub.oil.times.[1-exp(-t.sub.r /T.sub.1oil)] EQU +V.sub.gas (T.sub.2).times.HI.sub.gas.times.[1-exp(-t.sub.r /T.sub.1gas)] (8)
where T.sub.2 is the transverse relaxation time as described above. T.sub.1 is a different function of T.sub.2 for each fluid. By factoring the ratio of T.sub.1 /T.sub.2, the TOE Factor can be calculated based on T.sub.2 instead of T.sub.1 as follows: EQU TOE Factor =[1-exp(-t.sub.r /(Ratio*T.sub.2)] (9)
where Ratio is the ratio of T.sub.1 /T.sub.2 which is expected to be about 1.5 for clay and capillary bound fluid formations, but may be equal to 1 under other conditions. Applying this ratio results in polarization expressions (i.e., equations 7 and 9) that are based on either T.sub.1 or T.sub.2.
Most of the above-described methods for determining BFV suffer from at least the common problem that the entire T.sub.2 distribution must be obtained (for example, Sezginer, on the other hand, utilizes only part of the T.sub.2 distribution). Under some circumstances, for example, in logging-while-drilling, it simply may not be possible to acquire the necessary T.sub.2 distribution, or the motion of logging-while-drilling may degrade the measured data (e.g., such as when the techniques of Sezginer are applied). Under other circumstances, such as when high logging speed is required, it may not be practical to obtain the entire T.sub.2 distribution. Under still other circumstances, it only may be practical to obtain the initial amplitude of the NMR signal, in which case, known methods for determining BFV are not available. Moreover, well logging typically is a time intensive task, requiring large expenditures of effort to acquire well data.
For at least the foregoing reasons, it is an object of the present invention to provide methods for determining BFV utilizing NMR techniques when less than a substantial part of the T.sub.2 distribution is available.
It is also an object of the present invention to provide methods for determining BFV utilizing NMR techniques when high logging speed is required.
It is a further object of the present invention to provide methods for determining BFV utilizing NMR techniques in which only the initial amplitude of the NMR signal is obtained.
It is a still further object of the present invention to provide methods for determining BFV utilizing NMR techniques in which well logging time is reduced.